Krishna
1

Step 1:  Draw a figure from the given information.

GIVEN:  Height of the pole AB = 10 m

Angle between the rope and pole  \angle CAB\ =\ 30\degree

Length of the rope AC = ?

Step 2: Determine the length of the rope by using the trigonometric ratios.

EXAMPLE:  We need to find the rope length(hypotenuse)

So,  take \cos A = \frac{adjacent}{hypotenuse}

\cos 30\degree = \frac{AB}{AC} = \frac{10}{AC}

\frac{\sqrt{3}}{2} = \frac{10}{AC}   (Since \cos 30\degree = \frac{\sqrt{3}}{2})

AC = \frac{2*10}{\sqrt{3}}

Simplify

AC = \frac{20}{\sqrt{3}} \frac{\sqrt{3}}{\sqrt{3}} ( \because Rationalization)

AC = \frac{20\sqrt{3}}{3}

AC = \frac{20 * 1.732}{3} ( \because \sqrt{3} = 1.732 )

AC = 11.55 m

Length of the rope = 11.55 m